$4$: $,$ The president of a company has asked you to develop a model that will predict total sales for

proposed new retail store locations. You have access to the data file $($retail sales.xls$).$ The company

has obtained data from a sampling survey of households in each of the target sales areas for their

existing stores, and the variables retail sales $(Y)$ and income $(x)$ per household will be used to develop

the model. All variable are measured in USD $$.$

In this question use EXCEL directly and get the answers of the following questions:

a$)$ Plot Total sales against locations, and make brief conclusions;

b$)$ Estimate the linear regression model;

c$)$ Interpret the results.

d$)$ Test the significance of slope, ${}_2,$ of the model. Use $p-$value of the EXCEL output to interpret

the results.

e$)$ EXCELL also provide ANOVA table. Get coefficient of determination, $r^2,$ using information in

this TABLE $($Note you can get this information directly from output$),$ but here show how you

will use ANOVA to get $r^2.$

f$)$ How you can use the information from data and EXCEL regression output, to construct $95\%$

confidence interval of prediction of $E(\frac{Y}{x})$ when $x_0=5000,$ that is income per household is

Get the interval and interpret the results. $[$You will need to use the formula of standard

error of the estimator of the predictor, we showed this both in lecture, also you can refer to

Gujrati book$).$ Show how you calculated this standard error and applied it to get the

confidence interval.